Kennedy was signed by the Washington Senators in 1961 (Hmmm.. I wonder if they would have noticed him, had Richard Nixon been the president?), and played in the Nats’ system for 3 seasons, almost exclusively as a shortstop. He also played 14 games with the Senators in September 1962, and 36 games in 1963 (from late-May to early-July, and again in a September call-up).
In 1964, John was with the Senators for the entire season, sharing the 3rd base job with veteran Don Zimmer. Kennedy started half the team’s games there, with another 43 starts at shortstop, spelling Ed Brinkman. However, he only hit .230 with 7 homers, and struck out 119 times.
After the 1964 season, Kennedy was sent with pitcher Claude Osteen and cash to the Dodgers for slugging outfielder Frank Howard, 3rd baseman Ken McMullen, pitchers Pete Richert and Phil Ortega, and first base prospect Dick Nen.
In 1965, the Dodgers employed a carousel of 3rd baseman (I’m sure Night Owl can verify the carousel went on for years, until Ron Cey showed up). The pecking order seemed to be Junior Gilliam, Dick Tracewski, and then Kennedy. The following season, Kennedy and Gilliam each started 52 games at the hot corner, with 2nd baseman Jim Lefebvre also making a few dozen starts there. John was also Maury Wills’ backup at shortstop in 1966.
Kennedy appears as a Dodger in the 1967 Topps set, but a few days before the season he was traded to the Yankees, and served as the backup SS/3B for one season. The Yanks sent him down to the minors for all of 1968, resulting in his absence from the Topps set that year. (He had a card in all other sets from '64 to '73.)
John resurfaced in 1969 as a member of the expansion Seattle Pilots. He played 61 games, mostly as a pinch-hitter, but was also the 3rd or 4th option at shortstop and 3rd base, as the new team used 53 players that season. Kennedy split the first half of 1970 between the Milwaukee Brewers and their AAA team, then was traded to the Red Sox in mid-June.
John was a utility infielder for Boston for the next several seasons, and played his last game on June 16, 1974. He played for Boston’s AAA team for the remainder of the 1974 season, then was released in October, ending his 12-year career.